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Find the differential equation of all the straight lines touching the circle x2 + y2 = r2.

  • a)
    r2 (1+(dy/dx))2

  • b)
    3r2 (1+(dx/dy))2

  • c)
    2r2 (1+(dy/dx))2

  • d)
    r2 (1+(dx/dy))2

Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Find the differential equation of all the straight lines touching the ...
  1. Let y = mx + c be the equation of all the straight lines touching the circle.
    Given : The equation of the circle is x2 + y2 = r2----------> (1)
    The tangent to the circle is c2 = r2(1+m2)
    c = r√(1+m2)
    we know that y = mx + c---------->(2)
    y = mx + r√(1+m2) ---------->(3)
    y - mx = r√(1+m2)
    Differentiating wrt x we get dy/dx -m =0
    dy/dx = m
    Substituting this in equation (3)
    y - (dy/dx . x) = r√(1+(dy/dx)2)
    Squaring on both sides, we get
    y2 - (dy/dx . x)2 = [ r√(1+(dy/dx)2)]2
    [y - x(dy/dx)]2 = r2 (1+(dy/dx))is the required differential equation.
    Answer: The differential equation of all the straight lines touching the circle x2 + y2 = r2 is [y - x(dy/dx)]2 = r2 (1+(dy/dx))2​​​​​​
 
 
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Most Upvoted Answer
Find the differential equation of all the straight lines touching the ...
  1. Let y = mx + c be the equation of all the straight lines touching the circle.
    Given : The equation of the circle is x2 + y2 = r2----------> (1)
    The tangent to the circle is c2 = r2(1+m2)
    c = r√(1+m2)
    we know that y = mx + c---------->(2)
    y = mx + r√(1+m2) ---------->(3)
    y - mx = r√(1+m2)
    Differentiating wrt x we get dy/dx -m =0
    dy/dx = m
    Substituting this in equation (3)
    y - (dy/dx . x) = r√(1+(dy/dx)2)
    Squaring on both sides, we get
    y2 - (dy/dx . x)2 = [ r√(1+(dy/dx)2)]2
    [y - x(dy/dx)]2 = r2 (1+(dy/dx))is the required differential equation.
    Answer: The differential equation of all the straight lines touching the circle x2 + y2 = r2 is [y - x(dy/dx)]2 = r2 (1+(dy/dx))2​​​​​​
 
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Find the differential equation of all the straight lines touching the circle x2+ y2= r2.a)r2(1+(dy/dx))2b)3r2(1+(dx/dy))2c)2r2(1+(dy/dx))2d)r2(1+(dx/dy))2Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Find the differential equation of all the straight lines touching the circle x2+ y2= r2.a)r2(1+(dy/dx))2b)3r2(1+(dx/dy))2c)2r2(1+(dy/dx))2d)r2(1+(dx/dy))2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the differential equation of all the straight lines touching the circle x2+ y2= r2.a)r2(1+(dy/dx))2b)3r2(1+(dx/dy))2c)2r2(1+(dy/dx))2d)r2(1+(dx/dy))2Correct answer is option 'A'. Can you explain this answer?.
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